It is known that a supported ruthenium oxide is useful as a catalyst for use in production of chlorine by oxidizing hydrogen chloride with oxygen (see Patent Documents 1-5). As this supported ruthenium oxide, a supported ruthenium oxide in which ruthenium oxide and silica are supported on a titania carrier is known, and for its production process, for example, Patent Documents 6 and 7 disclose a process in which a titania carrier is brought into contact with a ruthenium compound, followed by being calcined, then is brought into contact with an alkoxysilane compound, followed by being dried in air, and then is calcined in air; and Patent Document 8 discloses a process in which a titania carrier is brought into contact with an alkoxysilane compound, followed by being dried in air, then is calcined in air, followed by being brought into contact with a ruthenium compound, and is calcined in air.